“I don’t think brave is the right word for it,” said one City Hall insider about the speaker’s tweet Sunday night that she had HPV, which in rare cases can lead to cervical cancer.

“It’s this new level of false intimacy on Twitter. The fact that it’s done on a Sunday night, it’s not really when you release news. Did I need to know? No,” the source said.

Others found it odd that Mark-Viverito, 45, would go public even before she has a biopsy to determine whether the virus had caused a cancerous or pre-cancerous condition.

“I thought she might wait until she gets her test results back and then sound the alarm. But screaming from the top of the mountain that she has HPV is TMI [too much information],” a council source said.

“That’s a strange forum to make such an announcement. It might end up being absolutely nothing. At what point is it appropriate to make an announcement?” another council source added.

But others defended the East Harlem Democrat, who dropped the bombshell that she had “high-risk HPV” from Puerto Rico, where she officiated at the wedding of a gay couple over the weekend.

“It’s about raising awareness and taking away stigmas. She did it when it felt right, it’s something that’s been clearly on her mind for a while,” said a Mark-Viverito aide, adding that the council speaker controls her own Twitter account. “She’s very real on [Twitter].”

Other city pols hailed Mark-Viverito, who had no comment when she returned to her East Harlem home Monday afternoon.

“Before this weekend, I had great respect for Melissa Mark-Viverito. My respect is even greater today,” Mayor de Blasio said.

Mark-Viverito, who isn’t married, tweeted Sunday that she’s an “extremely private person’’ — but her love of Twitter is famous. She added in a tweet that she’s getting a biopsy Tuesday.

Yes, I'm an extremely private person. But this position has led me to understand I now have a bigger responsibility. So….#moretocome

Roughly 79,000 Americans are believed to carry HPV, which is transmitted through oral, anal or vaginal sex.

Health experts say boys and girls should get vaccinated against the virus at age 11 or 12.

Dr. Constance Young, medical director for women’s health at Community Healthcare Network, said most infected American women have a low risk of cervical cancer if they are screened and receive proper medical treatment afterward.